A simpler and more efficient algorithm for the next-to-shortest path problem

Abstract

Given an undirected graph G = (V,E) with positive edge weights and two vertices s and t, the next-to-shortest path problem is to find an st-path which length is minimum among all st-paths of lengths strictly larger than the shortest path length. In this paper we give an O(|V|log|V|+|E|) time algorithm for this problem, which improves the previous result of O(|V|2) time for sparse graphs. © 2010 Springer-Verlag.